# Scattering and Gathering for Spatially Varying Blurs

arXiv: https://arxiv.org/abs/2303.05687 · HTML: https://mlsanity.com/paper/2303.05687/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2023.

## Built on by (most cited first, 6 of 6)

- [Spatio-Temporal Turbulence Mitigation: A Translational Perspective](https://mlsanity.com/paper/2401.04244/) (2024)
- [Learning Phase Distortion with Selective State Space Models for Video Turbulence Mitigation](https://mlsanity.com/paper/2504.02697/) (2025)
- [Resolution Limit of Single-Photon LiDAR](https://mlsanity.com/paper/2403.17719/) (2024)
- [ConVRT: Consistent Video Restoration Through Turbulence with Test-time Optimization of Neural Video Representations](https://mlsanity.com/paper/2312.04679/) (2023)
- [GRAFNet: Multiscale Retinal Processing via Guided Cortical Attention Feedback for Enhancing Medical Image Polyp Segmentation](https://mlsanity.com/paper/2602.15072/) (2026)
- [Restore What Matters: Lessons from Joint Restoration and Recognition](https://mlsanity.com/paper/2609.13791/) (2026)

## Abstract (arXiv)

A spatially varying blur kernel h(x,u) is specified by an input coordinate u ∈ ℝ2 and an output coordinate x ∈ ℝ2. For computational efficiency, we sometimes write h(x,u) as a linear combination of spatially invariant basis functions. The associated pixelwise coefficients, however, can be indexed by either the input coordinate or the output coordinate. While appearing subtle, the two indexing schemes will lead to two different forms of convolutions known as scattering and gathering, respectively. We discuss the origin of the operations. We discuss conditions under which the two operations are identical. We show that scattering is more suitable for simulating how light propagates and gathering is more suitable for image filtering such as denoising.